3.1323 \(\int (1-2 x)^3 (2+3 x)^6 (3+5 x) \, dx\)

Optimal. Leaf size=56 \[ -\frac{40 (3 x+2)^{11}}{2673}+\frac{214 (3 x+2)^{10}}{1215}-\frac{518}{729} (3 x+2)^9+\frac{2009 (3 x+2)^8}{1944}-\frac{49}{243} (3 x+2)^7 \]

[Out]

(-49*(2 + 3*x)^7)/243 + (2009*(2 + 3*x)^8)/1944 - (518*(2 + 3*x)^9)/729 + (214*(
2 + 3*x)^10)/1215 - (40*(2 + 3*x)^11)/2673

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Rubi [A]  time = 0.0824372, antiderivative size = 56, normalized size of antiderivative = 1., number of steps used = 2, number of rules used = 1, integrand size = 20, \(\frac{\text{number of rules}}{\text{integrand size}}\) = 0.05 \[ -\frac{40 (3 x+2)^{11}}{2673}+\frac{214 (3 x+2)^{10}}{1215}-\frac{518}{729} (3 x+2)^9+\frac{2009 (3 x+2)^8}{1944}-\frac{49}{243} (3 x+2)^7 \]

Antiderivative was successfully verified.

[In]  Int[(1 - 2*x)^3*(2 + 3*x)^6*(3 + 5*x),x]

[Out]

(-49*(2 + 3*x)^7)/243 + (2009*(2 + 3*x)^8)/1944 - (518*(2 + 3*x)^9)/729 + (214*(
2 + 3*x)^10)/1215 - (40*(2 + 3*x)^11)/2673

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Rubi in Sympy [A]  time = 12.4183, size = 49, normalized size = 0.88 \[ - \frac{40 \left (3 x + 2\right )^{11}}{2673} + \frac{214 \left (3 x + 2\right )^{10}}{1215} - \frac{518 \left (3 x + 2\right )^{9}}{729} + \frac{2009 \left (3 x + 2\right )^{8}}{1944} - \frac{49 \left (3 x + 2\right )^{7}}{243} \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  rubi_integrate((1-2*x)**3*(2+3*x)**6*(3+5*x),x)

[Out]

-40*(3*x + 2)**11/2673 + 214*(3*x + 2)**10/1215 - 518*(3*x + 2)**9/729 + 2009*(3
*x + 2)**8/1944 - 49*(3*x + 2)**7/243

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Mathematica [A]  time = 0.00326255, size = 62, normalized size = 1.11 \[ -\frac{29160 x^{11}}{11}-\frac{45198 x^{10}}{5}-9450 x^9+\frac{10179 x^8}{8}+8937 x^7+4368 x^6-\frac{10444 x^5}{5}-2340 x^4-208 x^3+448 x^2+192 x \]

Antiderivative was successfully verified.

[In]  Integrate[(1 - 2*x)^3*(2 + 3*x)^6*(3 + 5*x),x]

[Out]

192*x + 448*x^2 - 208*x^3 - 2340*x^4 - (10444*x^5)/5 + 4368*x^6 + 8937*x^7 + (10
179*x^8)/8 - 9450*x^9 - (45198*x^10)/5 - (29160*x^11)/11

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Maple [A]  time = 0.002, size = 55, normalized size = 1. \[ -{\frac{29160\,{x}^{11}}{11}}-{\frac{45198\,{x}^{10}}{5}}-9450\,{x}^{9}+{\frac{10179\,{x}^{8}}{8}}+8937\,{x}^{7}+4368\,{x}^{6}-{\frac{10444\,{x}^{5}}{5}}-2340\,{x}^{4}-208\,{x}^{3}+448\,{x}^{2}+192\,x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  int((1-2*x)^3*(2+3*x)^6*(3+5*x),x)

[Out]

-29160/11*x^11-45198/5*x^10-9450*x^9+10179/8*x^8+8937*x^7+4368*x^6-10444/5*x^5-2
340*x^4-208*x^3+448*x^2+192*x

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Maxima [A]  time = 1.34235, size = 73, normalized size = 1.3 \[ -\frac{29160}{11} \, x^{11} - \frac{45198}{5} \, x^{10} - 9450 \, x^{9} + \frac{10179}{8} \, x^{8} + 8937 \, x^{7} + 4368 \, x^{6} - \frac{10444}{5} \, x^{5} - 2340 \, x^{4} - 208 \, x^{3} + 448 \, x^{2} + 192 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)*(3*x + 2)^6*(2*x - 1)^3,x, algorithm="maxima")

[Out]

-29160/11*x^11 - 45198/5*x^10 - 9450*x^9 + 10179/8*x^8 + 8937*x^7 + 4368*x^6 - 1
0444/5*x^5 - 2340*x^4 - 208*x^3 + 448*x^2 + 192*x

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Fricas [A]  time = 0.182368, size = 1, normalized size = 0.02 \[ -\frac{29160}{11} x^{11} - \frac{45198}{5} x^{10} - 9450 x^{9} + \frac{10179}{8} x^{8} + 8937 x^{7} + 4368 x^{6} - \frac{10444}{5} x^{5} - 2340 x^{4} - 208 x^{3} + 448 x^{2} + 192 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)*(3*x + 2)^6*(2*x - 1)^3,x, algorithm="fricas")

[Out]

-29160/11*x^11 - 45198/5*x^10 - 9450*x^9 + 10179/8*x^8 + 8937*x^7 + 4368*x^6 - 1
0444/5*x^5 - 2340*x^4 - 208*x^3 + 448*x^2 + 192*x

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Sympy [A]  time = 0.112011, size = 60, normalized size = 1.07 \[ - \frac{29160 x^{11}}{11} - \frac{45198 x^{10}}{5} - 9450 x^{9} + \frac{10179 x^{8}}{8} + 8937 x^{7} + 4368 x^{6} - \frac{10444 x^{5}}{5} - 2340 x^{4} - 208 x^{3} + 448 x^{2} + 192 x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate((1-2*x)**3*(2+3*x)**6*(3+5*x),x)

[Out]

-29160*x**11/11 - 45198*x**10/5 - 9450*x**9 + 10179*x**8/8 + 8937*x**7 + 4368*x*
*6 - 10444*x**5/5 - 2340*x**4 - 208*x**3 + 448*x**2 + 192*x

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GIAC/XCAS [A]  time = 0.205531, size = 73, normalized size = 1.3 \[ -\frac{29160}{11} \, x^{11} - \frac{45198}{5} \, x^{10} - 9450 \, x^{9} + \frac{10179}{8} \, x^{8} + 8937 \, x^{7} + 4368 \, x^{6} - \frac{10444}{5} \, x^{5} - 2340 \, x^{4} - 208 \, x^{3} + 448 \, x^{2} + 192 \, x \]

Verification of antiderivative is not currently implemented for this CAS.

[In]  integrate(-(5*x + 3)*(3*x + 2)^6*(2*x - 1)^3,x, algorithm="giac")

[Out]

-29160/11*x^11 - 45198/5*x^10 - 9450*x^9 + 10179/8*x^8 + 8937*x^7 + 4368*x^6 - 1
0444/5*x^5 - 2340*x^4 - 208*x^3 + 448*x^2 + 192*x